Abstract
We consider the problem of optimal control of a flying object (FO) by the Pontryagin maximum principle with minimizing the control expenses. The dynamics of an FO in space is defined by Euler and Poisson equations. A two-point boundary value problem is solved with the Newton’s method. We give results of numerical modeling and recommendations to provide for convergence of the iterative procedure.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Krasovskii, A.A., Fast Numerical Integration of a Certain Class of Dynamical Systems, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1989, no. 1, pp. 3–14.
Krasovskii, A.A., Fundamentals of Algorithmic Issues of Automatic Flight Control with Deep Integration, in Voprosy kibernetiki: problemy kompleksirovaniya kiberneticheskikh dinamicheskikh sistem (Cybernetics Problems: Complexing Problems of Cybernetics Dynamics Systems), Moscow: Scientific Council on the Complex Problem “Cybernetics,” 1992, pp. 6–30.
Kabanov, S.A., A Sequential Optimization Algorithm with Spiral Forecast for Controlling a Landing Unit, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1993, no. 4, pp. 141–147.
Wang, H.M. and Kabanov, S.A., Optimal Control of the Return of a Flying Object on the Hierarchy of Criterion of Quality, 2002 FIRA Robot World Congr., Seoul, Korea, 2002, pp. 187–190.
Kabanov, S.A., Upravlenie sistemami na prognoziruyushchikh modelyakh (System Control on Forecasting Models), St. Petersburg: S.-Peterburg. Gos. Univ., 1997.
Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., et al., Matematicheskaya teoriya optimal’nykh protsessov (Mathematical Theory of Optimal Processes), Moscow: Fizmatlit, 1961.
Lebedev, A.A. and Chernobrovkin, L.S., Dinamika poleta BPLA (Dynamics of an Unmanned Flying Machine), Moscow: Mashinostroenie, 1973.
Aleksandrov, A.A. and Kabanov, S.A., Optimization of Landing of Unmanned Flying Machine in View of the Constraints on Control, Mekhatronika, Avtomatiz., Upravl., 2008, no. 2, pp. 50–54.
Fedorenko, R.P., Priblizhennoe reshenie zadach optimal’nogo upravleniya (Approximate Solutions for Optimal Control Problems), Moscow: Nauka, 1978.
Kabanov, S.A. and Aleksandrov, A.A., Prikladnye zadachi optimal’nogo upravleniya. Uch. pos. k praktich. zanyatiyam (Applied Optimal Control Problems. Practical Studies), St. Petersburg: Gos. Tekhn. Univ., 2007.
Author information
Authors and Affiliations
Additional information
Original Russian Text © S.A. Kabanov, A.A. Aleksandrov, 2010, published in Avtomatika i Telemekhanika, 2010, No. 1, pp. 46–56.
The work was supported by the Russian Foundation of Basic Research, project no. 09-08-00829.
Rights and permissions
About this article
Cite this article
Kabanov, S.A., Aleksandrov, A.A. Optimizing the trajectory of spatial movement of a flying object as a solid body. Autom Remote Control 71, 39–48 (2010). https://doi.org/10.1134/S0005117910010042
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117910010042